Question
Laura bought a roll of string to make friendship bracelets. She makes each bracelet the same length. The amount of string Laura has left depends on how many bracelets she has made.
There is a linear relationship between the number of bracelets Laura makes and the amount of string she has left, in meters.
Describe the rate of change for this relationship.
The amount of string left
by
per bracelet.
There is a linear relationship between the number of bracelets Laura makes and the amount of string she has left, in meters.
Describe the rate of change for this relationship.
The amount of string left
by
per bracelet.
Answers
GPT-4o mini
In a linear relationship, the rate of change represents the amount by which one quantity changes in relation to another. In this case, the relationship describes how the amount of string Laura has left changes as she makes more bracelets.
Let's say each bracelet requires a certain length of string, denoted as \( L \) meters. If Laura starts with an initial length of string, \( S_0 \) meters, and she makes \( n \) bracelets, the amount of string left can be described by the equation:
\[
S(n) = S_0 - nL
\]
In this equation:
- \( S(n) \) is the amount of string left after making \( n \) bracelets.
- \( S_0 \) is the initial amount of string Laura had.
- \( L \) is the amount of string used for each bracelet.
- \( n \) is the number of bracelets made.
The rate of change in this situation is essentially \( -L \). This means that for each bracelet Laura makes, the amount of string she has left decreases by \( L \) meters.
To summarize: The rate of change for this relationship is \(-L\) meters of string left per bracelet made, indicating that the amount of string decreases by \( L \) meters for every additional bracelet Laura creates.
Let's say each bracelet requires a certain length of string, denoted as \( L \) meters. If Laura starts with an initial length of string, \( S_0 \) meters, and she makes \( n \) bracelets, the amount of string left can be described by the equation:
\[
S(n) = S_0 - nL
\]
In this equation:
- \( S(n) \) is the amount of string left after making \( n \) bracelets.
- \( S_0 \) is the initial amount of string Laura had.
- \( L \) is the amount of string used for each bracelet.
- \( n \) is the number of bracelets made.
The rate of change in this situation is essentially \( -L \). This means that for each bracelet Laura makes, the amount of string she has left decreases by \( L \) meters.
To summarize: The rate of change for this relationship is \(-L\) meters of string left per bracelet made, indicating that the amount of string decreases by \( L \) meters for every additional bracelet Laura creates.